Which statistical measure assesses the goodness of fit for a regression model?

The measure that assesses the goodness of fit for a regression model is Adjusted R-squared. This statistic provides insight into how well the independent variables in the model explain the variability of the dependent variable. Unlike the regular R-squared, which can be artificially inflated by adding more predictors, Adjusted R-squared adjusts for the number of predictors in the model. This adjustment allows for a more accurate comparison of models with different numbers of independent variables, enabling researchers to ascertain if additional predictors actually improve the model's performance in explaining variance.

In practice, a higher Adjusted R-squared value indicates a better fit of the model to the observed data, suggesting that the predictors are effectively capturing the relationship with the outcome variable without simply adding complexity for the sake of it. This measure is particularly useful in regression analysis, where determining the appropriate model complexity is crucial.

The other statistical measures presented do not adequately reflect the goodness of fit. The standard deviation measures the spread of data points around the mean, percent variance describes proportionate changes in data but does not directly assess model fit. The correlation coefficient indicates the strength and direction of a linear relationship between two variables but does not account for model complexity or overall fit, making Adjusted R-squared the most relevant measure for